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added documentation and references

This commit is contained in:
Martin Diehl 2019-09-03 15:24:34 -07:00
parent 54dce38349
commit 7d48764999
1 changed files with 56 additions and 7 deletions
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63
python/damask/Lambert.py
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@ -1,5 +1,6 @@
####################################################################################################
# Code below available according to the followin conditions on https://github.com/MarDiehl/3Drotations
# Code below available according to the following conditions on
# https://github.com/MarDiehl/3Drotations
####################################################################################################
# Copyright (c) 2017-2019, Martin Diehl/Max-Planck-Institut für Eisenforschung GmbH
# Copyright (c) 2013-2014, Marc De Graef/Carnegie Mellon University
@ -36,7 +37,22 @@ beta = np.pi**(5./6.)/6.**(1./6.)/2.
R1 = (3.*np.pi/4.)**(1./3.)
def CubeToBall(cube):
"""
Map a point in a uniform refinable cubical grid to a point on a uniform refinable grid on a ball.
Parameters
----------
cube : numpy.ndarray
coordinates of a point in a uniform refinable cubical grid.
References
----------
D. Roşca, A. Morawiec, and M. De Graef
A new method of constructing a grid in the space of 3D rotations and its applications to texture analysis
Modelling Simul. Mater. Sci. Eng. 22, 2014, 075013
https://doi.org/10.1088/0965-0393/22/7/075013
"""
if np.abs(np.max(cube))>np.pi**(2./3.) * 0.5:
raise ValueError
@ -45,7 +61,7 @@ def CubeToBall(cube):
ball = np.zeros(3)
else:
# get pyramide and scale by grid parameter ratio
p = GetPyramidOrder(cube)
p = get_order(cube)
XYZ = cube[p] * sc
# intercept all the points along the z-axis
@ -74,7 +90,22 @@ def CubeToBall(cube):
def BallToCube(ball):
"""
Map a point on a uniform refinable grid on a ball to a point in a uniform refinable cubical grid.
Parameters
----------
ball : numpy.ndarray
coordinates of a point on a uniform refinable grid on a ball.
References
----------
D. Roşca, A. Morawiec, and M. De Graef
A new method of constructing a grid in the space of 3D rotations and its applications to texture analysis
Modelling Simul. Mater. Sci. Eng. 22, 2014, 075013
https://doi.org/10.1088/0965-0393/22/7/075013
"""
rs = np.linalg.norm(ball)
if rs > R1:
raise ValueError
@ -82,7 +113,7 @@ def BallToCube(ball):
if np.allclose(ball,0.0,rtol=0.0,atol=1.0e-300):
cube = np.zeros(3)
else:
p = GetPyramidOrder(ball)
p = get_order(ball)
xyz3 = ball[p]
# inverse M_3
@ -110,8 +141,26 @@ def BallToCube(ball):
return cube
def GetPyramidOrder(xyz):
def get_order(xyz):
"""
Get order of the coordinates.
Depending on the pyramid in which the point is located, the order need to be adjusted.
Parameters
----------
xyz : numpy.ndarray
coordinates of a point on a uniform refinable grid on a ball or
in a uniform refinable cubical grid.
References
----------
D. Roşca, A. Morawiec, and M. De Graef
A new method of constructing a grid in the space of 3D rotations and its applications to texture analysis
Modelling Simul. Mater. Sci. Eng. 22, 2014, 075013
https://doi.org/10.1088/0965-0393/22/7/075013
"""
if (abs(xyz[0])<= xyz[2]) and (abs(xyz[1])<= xyz[2]) or \
(abs(xyz[0])<=-xyz[2]) and (abs(xyz[1])<=-xyz[2]):
return [0,1,2]